English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

For a stationary and axisymmetric spacetime, the vacuum Einstein fieldequations reduce to a single nonlinear PDE in two dimensions called the Ernstequation. By solving this equation with a {\it Dirichlet} boundary conditionimposed along the disk, Neugebauer and Meinel in the 1990s famously derived anexplicit expression for the spacetime metric corresponding to theBardeen-Wagoner uniformly rotating disk of dust. In this paper, we consider asimilar boundary value problem for a rotating disk in which a {\it Neumann}boundary condition is imposed along the disk instead of a Dirichlet condition.Using the integrable structure of the Ernst equation, we are able to reduce theproblem to a Riemann-Hilbert problem on a genus one Riemann surface. By solvingthis Riemann-Hilbert problem in terms of theta functions, we obtain an explicitexpression for the Ernst potential. Finally, a Riemann surface degenerationargument leads to an expression for the associated spacetime metric.

Exact solution of a Neumann boundary value problem for the stationary axisymmetric Einstein equations